A227234 G.f.: Sum_{n>=1} x^n * (1+x)^prime(n).

1, 3, 5, 9, 19, 43, 109, 297, 793, 2059, 5382, 14319, 38897, 110525, 335225, 1067923, 3449922, 11058922, 35087589, 110642516, 346605981, 1072833978, 3270252617, 9869924183, 29933522269, 92890564700, 298225920323, 987831491085, 3330591758612, 11254395868044, 37691422431130, 124450270430236

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = Sum_{k=1..n} binomial(prime(k), n-k).

Example

G.f.: A(x) = x + 3*x^2 + 5*x^3 + 9*x^4 + 19*x^5 + 43*x^6 + 109*x^7 + 297*x^8 +...
where
A(x) = x*(1+x)^2 + x^2*(1+x)^3 + x^3*(1+x)^5 + x^4*(1+x)^7 + x^5*(1+x)^11 + x^6*(1+x)^13 + x^7*(1+x)^17 + x^8*(1+x)^19 +...+ x^n*(1+x)^prime(n) +...

Prog

(PARI) {a(n)=polcoeff(sum(m=1, n, x^m*(1+x+x*O(x^n))^prime(m)), n)}
for(n=1, 40, print1(a(n), ", "))
(PARI) {a(n) = sum(k=1, n, binomial(prime(k), n-k))}
for(n=1, 40, print1(a(n), ", "))

Crossrefs

Cf. A227235, A000040.

Sequence in context: A078066 A018002 A255822 * A192480 A107028 A147470

Adjacent sequences: A227231 A227232 A227233 * A227235 A227236 A227237

Keyword

nonn

Author

Paul D. Hanna, Jul 14 2013

Status

approved